I did the only right thing... Disassembled the diff again (for the third or forth time) and took out the pins. Compared the two pins - one was significantly longer than the other. Nothing that can't be fixed though. Shaved off some material from both ends so the pins were equally long. Now they both were easy to drop in, just a little push.

Edit: Hmmm... the diff is still not as good as the other one... Start to suspect it has been permanently damaged by the long pin.